**Correct Option: B. The volume is halved.** ### Detailed Explanation: **Understanding Boyle's Law:** Boyle's Law states that for a given mass of an ideal gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). This relationship can be mathematically expressed as: \[ P \propto \frac{1}{V} \] or, more commonly, in equation form: \[ PV = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. **What Happens When Pressure is Doubled:** 1. **Initial State:** Let's denote the initial pressure as \( P_1 \) and the initial volume as \( V_1 \). According to Boyle's Law, we have: \[ P_1 V_1 = k \] 2. **New State:** If the pressure is doubled, the new pressure \( P_2 \) becomes: \[ P_2 = 2P_1 \] 3. **Applying Boyle's Law Again:** We can apply Boyle's Law to the new state: \[ P_2 V_2 = k \] Substituting \( P_2 \) into the equation gives: \[ (2P_1) V_2 = k \] 4. **Relating the Two States:** Since we know that \( k = P_1 V_1 \), we can substitute this into the new equation: \[ (2P_1) V_2 = P_1 V_1 \] 5. **Solving for \( V_2 \):** Dividing both sides by \( 2P_1 \): \[ V_2 = \frac{P_1 V_1}{2P_1} = \frac{V_1}{2} \] This shows that when the pressure is doubled, the volume is halved. Thus, the correct answer is **B. The volume is halved.** ### Why Other Options Are Incorrect: - **Option A: The volume doubles.** - This option suggests that if pressure increases, volume also increases, which contradicts Boyle's Law. According to Boyle's Law, pressure and volume have an inverse relationship; if one increases, the other must decrease. - **Option C: The volume remains unchanged.** - This option implies that pressure changes do not affect volume, which is incorrect. Boyle's Law clearly states that volume changes in response to pressure changes when temperature is held constant. - **Option D: The volume increases by a factor of four.** - This option suggests a direct proportionality between pressure and volume, which is not the case. An increase in pressure leads to a decrease in volume, not an increase. ### Common Pitfalls: - **Confusing Direct and Inverse Relationships:** Students often confuse direct relationships (where both variables increase or decrease together) with inverse relationships (where one variable increases while the other decreases). Remember, Boyle's Law is an inverse relationship. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is constant. If temperature changes, other gas laws (like Charles's Law) must be considered. ### Revision Summary: - Boyle's Law states that pressure and volume of a gas are inversely related at constant temperature. - Doubling the pressure of a gas results in halving its volume. - The correct answer to the question is B: The volume is halved. - Remember to distinguish between direct and inverse relationships in gas laws.